sm.sigma {sm}

Estimation of the error standard deviation in nonparametric regression.

Description

This function estimates the error standard deviation in nonparametric regression with one or two covariates.

Usage

sm.sigma(x, y, rawdata = NA, weights = rep(1, length(y)), 
               diff.ord = 2, ci = FALSE, model = "none", h = NA, ...)
       

Arguments

x

a vector or two-column matrix of covariate values.

y

a vector of responses.

rawdata

a list containing the output from a binning operation. This argument is used by sm.regression and it need not be set for direct calls of the function.

weights

a list of frequencies associated with binned data. This argument is used by sm.regression and it need not be set for direct calls of the function.

diff.ord

an integer value which determines first (1) or second (2) differencing in the estimation of sigma.

ci

a logical value which controls whether a confidence interval is produced.

model

a character variable. If this is set to "constant" then a test of constant variance over the covariates is performed (only in the case of two covariates)

h

a vector of length two defining a smoothing parameter to be used in the test of constant variance.

...

other optional parameters are passed to the sm.options function, through a mechanism which limits their effect only to this call of the function; the only one relevant for this function is nbins.

Details

see the reference below.

Value

a list containing the estimate and, in the two covariate case, a matrix which can be used by the function sm.sigma2.compare, pseudo-residuals and, if appropriate, a confidence interval and a p-value for the test of constant variance.

Side Effects

none.

References

Bock, M., Bowman, A.W. & Ismail, B. (2007). Estimation and inference for error variance in bivariate nonparametric regression. Statistics & Computing, to appear.

See Also

sm.sigma2.compare

Examples

## Not run: 
with(airquality, {
   x     <- cbind(Wind, Temp)
   y     <- Ozone^(1/3)
   group <- (Solar.R < 200)
   sig1 <- sm.sigma(x[ group, ], y[ group], ci = TRUE)
   sig2 <- sm.sigma(x[!group, ], y[!group], ci = TRUE)
   print(c(sig1$estimate, sig1$ci))
   print(c(sig2$estimate, sig2$ci))
   print(sm.sigma(x[ group, ], y[ group], model = "constant", h = c(3, 5))$p)
   print(sm.sigma(x[!group, ], y[!group], model = "constant", h = c(3, 5))$p)
   print(sm.sigma2.compare(x[group, ], y[group], x[!group, ], y[!group]))
})

## End(Not run)